# sklearn.decomposition.dict_learning¶

sklearn.decomposition.dict_learning(X, n_components, *, alpha, max_iter=100, tol=1e-08, method='lars', n_jobs=None, dict_init=None, code_init=None, callback=None, verbose=False, random_state=None, return_n_iter=False, positive_dict=False, positive_code=False, method_max_iter=1000)[source]

Solves a dictionary learning matrix factorization problem.

Finds the best dictionary and the corresponding sparse code for approximating the data matrix X by solving:

(U^*, V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1
(U,V)
with || V_k ||_2 = 1 for all  0 <= k < n_components


where V is the dictionary and U is the sparse code. ||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix.

Read more in the User Guide.

Parameters
Xndarray of shape (n_samples, n_features)

Data matrix.

n_componentsint

Number of dictionary atoms to extract.

alphaint

Sparsity controlling parameter.

max_iterint, default=100

Maximum number of iterations to perform.

tolfloat, default=1e-8

Tolerance for the stopping condition.

method{‘lars’, ‘cd’}, default=’lars’

The method used:

• 'lars': uses the least angle regression method to solve the lasso

problem (linear_model.lars_path);

• 'cd': uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). Lars will be faster if the estimated components are sparse.

n_jobsint, default=None

Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

dict_initndarray of shape (n_components, n_features), default=None

Initial value for the dictionary for warm restart scenarios. Only used if code_init and dict_init are not None.

code_initndarray of shape (n_samples, n_components), default=None

Initial value for the sparse code for warm restart scenarios. Only used if code_init and dict_init are not None.

callbackcallable, default=None

Callable that gets invoked every five iterations

verbosebool, default=False

To control the verbosity of the procedure.

random_stateint, RandomState instance or None, default=None

Used for randomly initializing the dictionary. Pass an int for reproducible results across multiple function calls. See Glossary.

return_n_iterbool, default=False

Whether or not to return the number of iterations.

positive_dictbool, default=False

Whether to enforce positivity when finding the dictionary.

New in version 0.20.

positive_codebool, default=False

Whether to enforce positivity when finding the code.

New in version 0.20.

method_max_iterint, default=1000

Maximum number of iterations to perform.

New in version 0.22.

Returns
codendarray of shape (n_samples, n_components)

The sparse code factor in the matrix factorization.

dictionaryndarray of shape (n_components, n_features),

The dictionary factor in the matrix factorization.

errorsarray

Vector of errors at each iteration.

n_iterint

Number of iterations run. Returned only if return_n_iter is set to True.